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Trees

, Volume 24, Issue 1, pp 105–115 | Cite as

Numerical study of how creep and progressive stiffening affect the growth stress formation in trees

  • Sigurdur OrmarssonEmail author
  • Ola Dahlblom
  • Marie Johansson
Original Paper

Abstract

It is not fully understood how much growth stresses affect the final quality of solid timber products in terms of, e.g. shape stability. It is, for example, difficult to predict the internal growth stress field within the tree stem. Growth stresses are progressively generated during the tree growth and they are highly influenced by climate, biologic and material-related factors. To increase the knowledge of the stress formation, a finite element model was created to study how the growth stresses develop during the tree growth. The model is an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The material model used is based on the theory of small strains (where strains refer to the undeformed configuration which is good approximation for strains less than 4%) where so-called biological maturation strains (growth-related strains that form in the wood fibres during their maturation) are used as a driver for the stress generation. It is formulated as an incremental material model that takes into account elastic strain, maturation strain, viscoelastic strain and progressive stiffening of the wood material. The results clearly show how the growth stresses are progressively generated during the tree growth. The inner core becomes more and more compressed, whereas the outer sapwood is subjected to slightly increased tension. The parametric study shows that the growth stresses are highly influenced by the creep behaviour and evolution of parameters such as modulus of elasticity, micro-fibril angle and maturation strain.

Keywords

Growth stresses Trees Finite element simulations Wood Creep Distortions 

References

  1. Alhasani MA (1999) Growth stresses in Norway spruce. Licentiate thesis, report TVBK-1016, Lund University, Division of Structural Engineering, Lund, SwedenGoogle Scholar
  2. Alméras T, Gril J, Yamamoto H (2005) Modelling anisotropic maturation strain in wood in relation to fibre boundary conditions, microstructure and maturation kinetics. Holzforschung 59:347–353CrossRefGoogle Scholar
  3. Archer RR (1986) Growth stresses and strains in trees. Springer, BerlinGoogle Scholar
  4. Archer RR (1987) On the origin of growth stresses in trees. Part 1. Micromechanics of the developing cambial cell wall. Wood Sci Technol 21:139–154CrossRefGoogle Scholar
  5. Archer RR, Byrnes FE (1974) On the distribution of tree growth stresses. Part 1. An anisotropic plane strain theory. Wood Sci Technol 8:184–196CrossRefGoogle Scholar
  6. Bamber RK (1978) Origin of growth stresses. Forpride Digest 8(1):75–96Google Scholar
  7. Boyd JD (1950) Tree growth stresses III. The origin of growth stresses. Aust J Sci Res B Biol Sci 3(3):294–309Google Scholar
  8. CALFEM (2004) A finite element toolbox to MATLAB, version 3.4. http://www.byggmek.lth.se/Calfem
  9. Dahlblom O, Petersson H, Ormarsson S (1999a) Characterization of modulus of elasticity, European project FAIR CT 96-1915, improved spruce timber utilization, final report sub-task AB1.7Google Scholar
  10. Dahlblom O, Petersson H, Ormarsson S (1999b) Characterization of shrinkage, European project FAIR CT 96-1915, improved spruce timber utilization, final report sub-task AB1.5Google Scholar
  11. Fourcaud T, Lac P (2003) Numerical modelling of shape regulation and growth stresses in trees, I. An incremental static finite element formulation. Trees 17:23–30CrossRefGoogle Scholar
  12. Fourcaud T, Blaise F, Lac P, Castéra P, de Reffye P (2003) Numerical modelling of shape regulation and growth stresses in trees, II. Implementation in the AMAPpara software and simulation of tree growth. Trees 17:31–39CrossRefGoogle Scholar
  13. Fournier M, Bordonne PA, Guitard D, Okuyama T (1990) Growth stress patterns in tree stems—a model assuming evolution with the tree age of maturation strains. Wood Sci Technol 24:131–142CrossRefGoogle Scholar
  14. Fournier M, Bailleres H, Canson B (1994) Tree biomechanics: growth, cumulative prestresses, and reorientations. Biomimetics 2(3):229–251Google Scholar
  15. Gressel P (1984) Zur Vorhersage des langfristigen Formänderungsverhaltens aus Kurz-Kriechversuchen. Holz Roh Werkst 42:293–301CrossRefGoogle Scholar
  16. Guitard D, Masse H, Yamamoto H, Okuyama T (1999) Growth stress generation: a new mechanical model of the dimensional change of wood cells during maturation. J Wood Sci Technol 45:384–391CrossRefGoogle Scholar
  17. Johansson M, Ormarsson S (2009) Influence of growth stresses and material properties on distortion of sawn timber—numerical investigation. Ann For Sci 66(6)Google Scholar
  18. Kübler H (1959a) Studies on growth stress in trees—part I: the origin of growth stresses and the stresses in transverse direction (Studien über Wachstumsspannung des Holzes—Erste Mitteilung: Die Ursache der Wachstumsspannungen und die Spannungen quer zur Faserrichtung). Holz als Roh- und Werkstoff 17(1):1–9 (in German)CrossRefGoogle Scholar
  19. Kübler H (1959b) Studies on growth stress in trees—part II: longitudinal stresses (Studien über Wachstumsspannung des Holzes—Zweite Mitteilung: Die Spannungen in Faserrichtung). Holz als Roh- und Werkstoff 17(2):44–54 (in German)CrossRefGoogle Scholar
  20. Kübler H (1987) Growth stresses in trees and related wood properties. For Prod Abstr 10(3):62–119Google Scholar
  21. Ormarsson S (1999) Numerical analysis of moisture-related distortion in sawn timber. Doctoral Thesis, Publ 99:7, Chalmers University of Technology, Department of Structural Mech, Göteborg, SwedenGoogle Scholar
  22. Ormarsson S, Johansson M (2006) Finite element simulation of growth stress formation and related board distortions resulting from sawing and forced drying. N Z J For Sci 36(2):408–423Google Scholar
  23. Ormarsson S, Dahlblom O, Johansson M (2009) Finite element study of growth stress formation in wood and related distortion of sawn timber. Wood Sci Technol 43(5):387–403CrossRefGoogle Scholar
  24. Ottosen NS, Ristinmaa M (2005) The mechanics of constitutive modeling. Elsevier, OxfordGoogle Scholar
  25. Persson K (2000) Micromechanical modelling of wood and fibre properties. Doctoral thesis, Publ. TVSM-1013, Division of Structural Mechanics, Lund University, SwedenGoogle Scholar
  26. Plomion C, Leprovost G, Stokes A (2001) Wood formation in trees. Plant Physiol 127:1513–1523CrossRefPubMedGoogle Scholar
  27. Raymond CA, Kube PD, Pinkard L, Savage L, Bradley AD (2004) Evaluation of non-destructive methods of measuring growth stress in eucalyptus globules: relationships between strain, wood properties and stress. For Ecol Manag 190:187–200CrossRefGoogle Scholar
  28. Skatter S, Archer RR (2001) Residual stresses caused by growth stresses within a stem with radially varying spiral grain angle—two numerical solution approaches: (1) finite element method and (2) transfer matrix method. Wood Sci Technol 35:57–71CrossRefGoogle Scholar
  29. Yamamoto H (1998) Generation mechanism of growth stresses in wood cell walls: roles of lignin deposition and cellulose microfibril during cell wall maturation. Wood Sci Technol 32:171–182Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Sigurdur Ormarsson
    • 1
    Email author
  • Ola Dahlblom
    • 2
  • Marie Johansson
    • 3
  1. 1.Department of Civil EngineeringTechnical University of DenmarkLyngbyDenmark
  2. 2.Division of Structural MechanicsLund UniversityLundSweden
  3. 3.School of Technology and DesignVäxjö UniversityVäxjöSweden

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